**Solution**

Given,

Diameter of 15^{th} ring (D_{15}) = 0.590 cm,

Diameter of 5^{th} ring (D_{5}) = 60 cm = 0.6 m,

Wavelength of light (λ) = 5580 Å = 5580 x 10^-8 cm

Radius of curvature (R) = ?,

m = 15,

n = 5

We have,

\(R=\frac{D_m^2-D_n^2}{4\lambda\left(m-n\right)}\)

= \(\frac{D_{15}^2-D_5^2}{4\lambda\left(15-5\right)}\)

= 100 cm

= 1 m

Therefore, the radius of curvature of the plano-convex lens is 1m.